Adder

ABSTRACT

According to an embodiment, an adder includes first and second wave computing units and a threshold wave computing unit. Each of the first and second wave computing units includes a pair of first input sections, a first wave transmission medium having a continuous film including a magnetic body connected to the first input sections, and a first wave detector outputting a result of computation by spin waves induced in the first wave transmission medium by the signals corresponding to the two bit values. The threshold wave computing unit includes a plurality of third input sections, a third wave transmission medium having a continuous film including a magnetic body connected to the third input sections, and a third wave detector a result of computation by spin waves induced in the third wave transmission medium.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuous application of International ApplicationPCT/JP2009/066291, filed on Sep. 17, 2009; the entire contents of whichare incorporated herein by reference.

FIELD

Embodiments described herein relate to an adder and, more particularly,to an adder using wave phenomena in a solid for logic operation.

BACKGROUND

An adder is one of the arithmetic logic units used in a computer. Theadder performs multi-bit addition operation for e.g. integer andfixed-point or floating-point values. Furthermore, the adder also servesas a component of other arithmetic logic units, such as a subtractor andmultiplier. Thus, the adder is required to have versatility and highspeed performance.

In a multi-bit adder, the propagation time of a carry signal from a lesssignificant position to a more significant position limits the overallprocessing speed of the adder. Thus, circuit techniques such as thecarry look-ahead scheme for performing carry operation for a moresignificant position in advance have been used to enhance the speed. Onthe other hand, from the viewpoint of increasing the operating speed ofthe logic element itself, miniaturizing the CMOS device have been usedto enhance its operating speed.

However, the circuit size is increased in the CMOS circuit equipped withthe carry look-ahead scheme. Furthermore, the physical limit in theminiaturization technology is also coming into sight as an inevitablereality. Moreover, with the increase in circuit size and theminiaturization, the increase in dynamic power consumption due toparasitic capacitance and the increase in static power consumption dueto leakage current are emerging as major problems. Thus, there is astrong demand for a technique for limiting the power consumption towithin a desired range to enhance the speed of computation processing.

One of the potential approaches aiming to break the limits of existingtechniques is the so-called “Beyond CMOS” technology, which is notnecessarily based on the Boolean algebra and CMOS architecture. Thistechnology includes approaches for information processing without chargemovement, such as optics, magnetic spin, and biotechnology. Inparticular, the spin wave is a space-time fluctuation of a magneticmoment in a magnetic body. The spin wave can be generated by low energyin principle, and is a high-speed oscillation phenomenon above GHz.Thus, a spin wave-based logic element is a promising candidate forfuture practical application as a power-saving information processingdevice. Examples of the spin wave-based logic element are disclosed inUnited States Patent Application Publication No. 2007/0296516 andApplied Physics Letters 87, 153501 (2005). However, the method forconfiguring an adder with suppressed increase in circuit size has notbeen known.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram schematically illustrating a 1-bit adderaccording to a first embodiment;

FIG. 2 is a block diagram schematically illustrating a variation of the1-bit adder according to the first embodiment;

FIGS. 3A and 3B are schematic views illustrating one of the computingunits 1 and 2 according to the first embodiment;

FIGS. 4A to 4C are schematic views illustrating partial cross-sectionsincluding an input section in the computing units 1 and 2 according tothe first embodiment;

FIGS. 5A to 5C are schematic views illustrating partial cross-sectionsincluding a wave detector in the computing units 1 and 2 according tothe first embodiment;

FIG. 6 is a schematic view illustrating a partial cross section of anadder according to the first embodiment;

FIGS. 7A and 7B are schematic diagrams illustrating examples of avoltage signal outputted from the computing units 1 and 2 according tothe first embodiment;

FIGS. 8A to 8D are schematic plan views illustrating examples of thecomputing units 1 and 2 according to the first embodiment;

FIGS. 9A to 9D are timing charts illustrating a relationship betweeninput signals and an output signal in the computing units 1 and 2according to the first embodiment;

FIGS. 10A to 10D are alternative timing charts illustrating arelationship between input signals and an output signal in the computingunits 1 and 2 according to the first embodiment;

FIG. 11 is a plan view schematically illustrating an alternative exampleof the computing units 1 and 2 according to the first embodiment;

FIGS. 12A to 12D are timing charts illustrating alternative example ofthe computing units 1 and 2 according to the first embodiment;

FIGS. 13A and 13B are schematic views illustrating examples of acomputing unit 3 according to the first embodiment;

FIGS. 14A to 15D are timing charts illustrating a relationship betweeninput signals and an output signal in the computing unit 3 according tothe first embodiment;

FIGS. 16A to 16D are schematic views illustrating partial cross-sectionsincluding an input section in a computing unit according to a variationof the first embodiment;

FIG. 17 is a schematic cross-sectional view illustrating the computingunit according to the variation of the first embodiment;

FIGS. 18A to 18C are schematic views illustrating partial cross-sectionsincluding an input section in a computing unit according to a secondvariation of the first embodiment;

FIG. 19A is a schematic cross-sectional view and FIG. 19B is a schematicplan view respectively, illustrating the computing unit according to thesecond variation of the first embodiment;

FIGS. 20A and 20B are schematic views illustrating partialcross-sections of a computing unit according to a third variation of thefirst embodiment;

FIG. 21 is a schematic view illustrating a partial cross section of acomputing units 1 and 2 according to a fourth variation of the firstembodiment

FIG. 22 is a perspective view schematically illustrating a computingunit according to a fifth variation;

FIGS. 23A and 23B are schematic views illustrating a computing unit 3according to a sixth variation;

FIG. 24 is a block diagram illustrating an adder according to a secondembodiment;

FIG. 25 is a block diagram illustrating a 2-bit adder according to thesecond embodiment;

FIG. 26 is a plan view schematically illustrating a computing unit ofthe 2-bit adder according to the second embodiment;

FIG. 27 is a block diagram illustrating an adder according to a thirdembodiment;

FIG. 28 is a block diagram illustrating a 4-bit sub-adder according tothe third embodiment.

DETAILED DESCRIPTION

According to an embodiment, an adder includes a first wave computingunit, a second wave computing unit and a threshold wave computing unit.The first wave computing unit includes a pair of first input sectionsreceiving signals corresponding to two bit values selected fromA[i+k−1], B[i+k−1] and C[i+k−2], wherein the A[i+k−1] is the bit valueof the (i+k−1)-th position of a binary value A; the B[i+k−1] is the bitvalue of the (i+k−1)-th position of the binary value B; and the C[i+k−2]is a carry bit value from the (i+k−2)-th position to the (i+k−1)-thposition resulting from addition of the binary value A and the binaryvalue B (i and k being integers). The first wave computing unit includesa first wave transmission medium having a continuous film including amagnetic body connected to the first input sections and a first wavedetector outputting X(k−1) as a result of computation by spin wavesinduced in the first wave transmission medium by the signalscorresponding to the two bit values. The second wave computing unitincludes a pair of second input sections receiving a signalcorresponding to the bit value not selected as the input to the firstinput sections among the A[i+k−1], B[i+k−1] and C[i+k−2], and the outputX(k−1), a second wave transmission medium having a continuous filmincluding a magnetic body connected to the second input sections, and asecond wave detector outputting S(k−1) as a result of computation byspin waves induced in the second wave transmission medium by the signalcorresponding to the bit value not selected and the output X(k−1). Thethreshold wave computing unit includes a plurality of third inputsections receiving signals corresponding to the A[i] to A[i+k−1], theB[i] to B[i+k−1], and the carry bit value C[i−1], a third wavetransmission medium having a continuous film including a magnetic bodyconnected to the third input sections, and a third wave detectoroutputting C(k−1) as a result of computation by spin waves induced inthe third wave transmission medium by the signals corresponding to theA[i] to A[i+k−1], B[i] to B[i+k−1], and C[i−1].

Embodiments of the invention will now be described with reference to thedrawings. In the following embodiments, like portions in the drawingsare labeled with like reference numerals, and the detailed descriptionthereof is omitted as appropriate. The different portions are describedas appropriate.

An adder according to an embodiment of the invention includes a firstwave computing unit, a second wave computing unit, and a threshold wavecomputing unit.

The first wave computing unit includes a pair of first input sections, afirst wave transmission medium connected to the first input section, anda first wave detector. The first input sections receives input ofsignals corresponding to two bit values selected from bit valuesA[i+k−1], B[i+k−1], and C[i+k−2]. The bit values A[i+k−1] and B[i+k−1]are taken from among the bit values of the i-th to (i+m−1)-th positionsof binary values A and B (where i and m are integers). The bit valueC[i+k−2] is the carry bit value from the (i+k−2)-th position to the(i+k−1)-th position resulting from the addition of the two binary valuesA and B. Here, the least significant position is referred to as zerothposition. The i-th position refers to the (i+1)-th bit counting from theleast significant position. Furthermore, k is an integer of 1 to m.

On the other hand, the first wave detector outputs X(k−1) as a result ofcomputation by waves induced in the first wave transmission medium bythe signals corresponding to the two bit values inputted to the firstinput sections.

The second wave computing unit includes a pair of second input sections,a second wave transmission medium connected to the second inputsections, and a second wave detector. The second input sections receivea signal corresponding to the bit value not selected as the input to thefirst input sections among A[i+k−1], B[i+k−1] and C[i+k−2], and theoutput X(k−1) of the first wave computing unit. On the other hand, thesecond wave detector outputs S(k−1) as a result of computation by wavesinduced in the second wave transmission medium by the signalcorresponding to the unselected bit value and the output X(k−1).

Furthermore, the threshold wave computing unit includes a plurality ofthird input sections, a third wave transmission medium connected to thethird input sections, and a third wave detector. The third inputsections receive signals corresponding to the bit values A[i] toA[i+k−1], the bit values B[i] to B[i+k−1], and the carry bit valueC[i−1]. The bit values A[i] to A[i+k−1] and the bit values B[i] toB[i+k−1] are the bit values of the i-th to (i+k−1)-th positions of thebinary values A and B. On the other hand, the third wave detectoroutputs C(k−1) as a result of computation by waves induced in the thirdwave transmission medium by the signals corresponding to A[i] toA[i+k−1], B[i] to B[i+k−1], and C[i−1].

(First Embodiment)

FIG. 1 is a block diagram schematically showing the configuration of a1-bit adder according to a first embodiment. In particular, FIG. 1corresponds to the case of m=1, k=1. A(0) and B(0) are signalscorresponding to the bit value A[i] and the bit value B[i] of the i-thposition of n-bit (n is an integer of 1 or more) binary values A and B.C(−1) is the carry signal from a less significant position correspondingto the carry bit value C[i−1] from the (i−1)-th position to the i-thposition. These are all given as electrical signals for one of theinputs represented by “0” corresponding to the bit value 0 or “1”corresponding to the bit value 1. Here, i is one of the integers 0 ton−1. For i equal to 0, C(−1) is an electrical signal corresponding to“0”.

The computing units 1, 2, and 3 shown in FIG. 1 are multi-input logicunits. The computing unit 1 is the first wave computing unit. Inresponse to input of A(0) and B(0), the computing unit 1 outputs anintermediate output X(0). The computing unit 2 is the second wavecomputing unit. The computing unit 2 receives as input the outputs X(0)and C(−1) of the computing unit 1, and outputs S(0). The computing unit3 is the threshold wave computing unit. The computing unit 3 receivesA(0), B(0), and C(−1) as input, and outputs C(0).

TABLE 1 is the truth table of the computing unit 1, and TABLE 2 is thetruth table of the computing unit 2. That is, the computing units 1 and2 perform exclusive OR operation. TABLE 3 shows the truth table of thecomputing unit 3. The computing unit 3 performs a threshold logicoperation. More specifically, the computing unit 3 performs theoperation of outputting 1 if the sum of the three numbers is 2 or more,and outputting 0 if the sum is 1 or less. These truth tables show thebit values A[i], B[i] of the binary values A and B, the carry bit valueC[i−1], and the bit values S[i], X[i], and C[i] corresponding to thecomputation results. These tables correspond to the relationshipsbetween the signals A(0), B(0), and C(−1) inputted to the computingunits and the computation results S(0), X(0), and C(0). This alsoapplies to TABLES 4 to 7 described below.

TABLE 1 A[i] B[i] X[i] 0 0 0 1 0 1 0 1 1 1 1 0

TABLE 2 X[i] C[i − 1] S[i] 0 0 0 1 0 1 0 1 1 1 1 0

TABLE 3 A[i] B[i] C[i − 1] C[i] 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 0 1 01 0 1 1 0 1 1 1 1 1 1 1

TABLE 4 is the truth table summarizing the relationship between theinputs and the outputs of the computing units 1, 2, and 3 according tothis embodiment. As seen from TABLE 4, the output does not change evenif A(0), B(0), and C(−1) are interchanged. For instance, even if B(0)and C(−1) are interchanged, the outputs S(0) and C(0) remain the same.

TABLE 4 A[i] B[i] C[i − 1] S[i] C[i] 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 11 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1

FIG. 2 is a block diagram schematically showing a variation of the 1-bitadder according to the first embodiment. This variation is configured sothat the inputs B(0) and C(−1) of the adder shown in FIG. 1 areinterchanged. That is, in this configuration, A(0) and C(−1) areinputted to the computing unit 1, and the output X(0) of the computingunit 1 and B(0) are inputted to the computing unit 2.

Next, the configuration of the computing units 1 to 3 according to theembodiment is described.

These computing units include, as their components, film-like media(hereinafter referred to as continuous films) serving as the first wavetransmission media to the third wave transmission media, the first inputsections to the third input sections to which electrical signalscorresponding to the input bit values of the computing unit can beapplied respectively, and the first wave detector to the third wavedetector provided on the respective continuous films, and each of thewave detectors is capable of extracting an electrical signalcorresponding in magnitude to the local amplitude of the wave.

(Example of the Wave Computing Unit)

FIGS. 3A and 3B are schematic views showing one of the computing units 1and 2 according to the embodiment. FIG. 3A shows a front view, and FIG.3B shows a plan view.

The computing unit shown in FIGS. 3A and 3B is a wave computing unit. Acontinuous film 11 is provided on a substrate, not shown. Two inputsections 5 and a wave detector 8 for detecting a spin wave are providedon the continuous film 11. The continuous film 11 includes at least onemagnetic layer exhibiting ferromagnetism at room temperature.

The input section 5 is provided so as to have a prescribed contactinterface with the continuous film 11. The input section 5 applies avoltage or passes a current in a direction generally perpendicular tothe surface of the continuous film 11. This generates spin torque in aregion immediately below the input section 5. Thus, a spin wave can beexcited in the magnetic layer constituting the continuous film 11 and ahalf wavelength of the spin wave is almost the same as the diameter ofthe contact interface. The excited spin wave propagates outward from theinput section 5 in the magnetic layer through the magnetostaticinteraction or the exchange interaction.

The contact interface at which the input section 5 and the continuousfilm 11 are electrically connected is preferably smaller than a circlehaving a diameter of 200 nm. If the contact interface is larger than acircle having a diameter of 200 nm, a vortex-like or multi-domainmagnetization structure is excited. This produces a complicatedstructure in which the spin wave includes a plurality of components, andthe spin wave becomes difficult to control. Furthermore, by downsizingthe input section 5, the overall computing unit can be downsized.

For these reasons, the contact interface of the input section 5 ispreferably shaped like an ellipse, circle, or polygon having a majorside length of 200 nm or less. Within this range, the computation by theexcited spin waves is easy to control.

FIGS. 4A to 4C are schematic views showing partial cross sections of theinput section 5 and the continuous film 11. In the cross-sectionalstructure shown in FIG. 4A, the continuous film 11 is configured in alayer structure of a magnetic layer 13, a spacer layer 14, and amagnetic layer 15 from the surface. The input section 5 is made of anon-magnetic conductive material. The input section 5 is provided on thesurface of the continuous film 11.

The magnetic layer 13 serves as a transmission medium for the spin wave.The current flowing from the input section 5 via the magnetic layer 13causes the magnetic layer 15 to impart spin torque to the magnetic layer13 and to excite a spin wave. The spin torque imparted to the magneticlayer 13 depends on the angle between the magnetization direction M2 ofthe magnetic layer 13 and the magnetization direction M1 of the magneticlayer 15. When this angle is 0° or 180°, the magnitude of the spintorque is small. Thus, the spin wave is excited when the large enoughcurrent is supplied. On the other hand, the spin torque continuouslychanges while the angle between M1 and M2 changes from 0° to 180°.Within this range, there exists an angle between M1 and M2 maximizingthe spin torque.

The polarity of the voltage applied to the input section 5, or thedirection of the current flowing between the input section 5 and themagnetic layer 15, in relation to the magnetization directions of themagnetic layers 13 and 15, are preferably selected so as to increase thespin torque.

The angle maximizing the spin torque may be included in the range of themagnetization direction M1 of the magnetic layer 15 being 60° to 120°with respect to the magnetization direction M2 of the magnetic layer 13.Hence, by setting the angle between M1 and M2 to within this range, aconfiguration of imparting spin torque can be realized with lowercurrent.

For instance, in the structure shown in FIG. 4A, the magnetizationdirection M2 of the magnetic layer 13 is directed parallel to thesurface of the continuous film 11. The magnetization direction M1 of themagnetic layer 15 is directed perpendicular to the surface of thecontinuous film. In FIG. 4B, the magnetization direction M2 of themagnetic layer 13 and the magnetization direction M1 of the magneticlayer 15 are both directed parallel to the surface of the continuousfilm 11, and may be made roughly orthogonal to each other in the planeof the continuous film 11. In FIG. 4C, the magnetization direction M2 ofthe magnetic layer 13 is made perpendicular to the surface of thecontinuous film 11. The magnetization direction of the magnetic layer 15is made parallel to the surface of the continuous film 11.

Among the structures shown in FIGS. 4A to 4C, the magnetizationdirection M2 of the magnetic layer 13 is preferably made roughlyperpendicular to the surface of the continuous film 11 as in FIG. 4C.This can provide the advantage that the propagation characteristic ofthe spin wave is isotropic in the plane of the continuous film 11 andindependent of the propagation direction. Furthermore, the magneticlayer 13 is a spin wave transmission medium. Thus, the magnetic layer 13is preferably made of a material being capable of efficiently receivingspin torque and having low transmission loss.

Examples of the magnetic material magnetized perpendicular to thesurface of the continuous film 11 can include alloys such as FeVPd,FeCrPd, and CoFePt. Alternatively, a ferrite oxide such as yttrium irongarnet (YIG) and manganese ferrite can be used to reduce thetransmission loss of the spin wave.

On the other hand, the magnetic layer 15 preferably has a pinnedmagnetization direction in order to impart a fixed spin torque to themagnetic layer 13. To this end, the layer thickness of the magneticlayer 15 is preferably set to 10 nm or more. Alternatively, as shown inFIGS. 4B and 4C, an antiferromagnetic layer 16 can be provided adjacentto the magnetic layer 15 to pin the magnetization direction M1 of themagnetic layer 15.

The material of the magnetic layer with the magnetization direction maderoughly parallel to the surface of the continuous film 11 can be amagnetic alloy containing at least one element selected from the groupconsisting of iron (Fe), cobalt (Co), nickel (Ni), manganese (Mn), andchromium (Cr), for example. The antiferromagnetic layer 16 may be madeof an IrMn alloy.

The spacer layer 14 is provided to be thinner than the length by whichthe electron loses its spin polarization, while moving between themagnetic layer 13 and the magnetic layer 15, i.e. the spin diffusionlength. Furthermore, the continuous film 11 may include, as theuppermost layer, a protective film formed on the magnetic layer 13.Preferably, in order to efficiently excite a spin wave, the protectivefilm is conductive and has a thickness of 100 nm or less.

The spacer layer 14 may be made of a tunnel barrier material or anon-magnetic metal material. By using a tunnel barrier material, a largereproduction signal can be obtained as the output at read time. Forinstance, the tunnel barrier material can be an oxide, nitride,fluoride, or oxynitride containing at least one element selected fromthe group consisting of aluminum (Al), titanium (Ti), zinc (Zn),zirconium (Zr), tantalum (Ta), cobalt (Co), nickel (Ni), silicon (Si),magnesium (Mg), and iron (Fe). Alternatively, it is also possible to usea semiconductor having a large energy gap such as GaAlAs.

On the other hand, a non-magnetic metal material can be used for thespace layer 14 to facilitate current injection for generating spintorque. For instance, the non-magnetic metal material may be selectedfrom a group of copper (Cu), gold (Au), silver (Ag), aluminum (Al), andan alloy that contains at least one element of Cu, Au, Ag and Al. Inthis case, setting the thickness of the spacer layer to 1.5 nm or moreand 20 nm or less can avoid interlayer coupling between the magneticlayer 13 and the magnetic layer 15, and retain the spin polarization ofelectrons.

Furthermore, the protective film provided on the uppermost layer of thecontinuous film 11 can be made of a material such as Ta, Ru, copper(Cu), gold (Au), silver (Ag), aluminum (Al), grapheme and an alloy thatcontains at least one element selected from the group of Ta, Ru, Cu, Au,Ag and Al.

The non-magnetic conductive material used for the input section 5 can bee.g. copper (Cu), gold (Au), silver (Ag), aluminum (Al), or an alloythat contains at least one element selected from the group consistingthereof. Alternatively, the non-magnetic conductive material can be amaterial such as carbon nanotube, carbon nanowire, and graphene.

FIGS. 5A to 5C are schematic views showing partial cross sections of thewave detector 8 and the continuous film 11. The wave detector 8 isprovided on the continuous film 11 via a contact interface. The spinwave generated immediately below the input section 5 and propagated inthe continuous film 11 is detected as a composite signal in the wavedetector 8. The each set of magnetization directions in FIGS. 5A to 5Ccorrespond respectively to the structures of the partial cross sectionsof the continuous film 11 shown in FIGS. 4A to 4C. That is, on the inputsection 5 side and on the wave detector 8 side, the magnetizationdirections of the magnetic layers 13 and 15 included in the continuousfilm 11 are the same.

In FIG. 5A, the magnetization direction M1 of the magnetic layer 15 isdirected perpendicular to the surface of the continuous film 11. Themagnetization direction M2 of the magnetic layer 13 is directed parallelto the surface of the continuous film 11. In FIG. 5B, the magnetizationdirection M1 of the magnetic layer 15 and the magnetization direction M2of the magnetic layer 13 are both parallel to the surface of thecontinuous film 11. Furthermore, M1 and M2 are orthogonal in the planeof the continuous film 11. In FIG. 5C, the magnetization direction M1 ofthe magnetic layer 15 is parallel to the surface of the continuous film11. The magnetization direction M2 of the magnetic layer 13 is directedperpendicular to the surface of the continuous film 11.

The continuous film 11 shown in FIGS. 5A to 5C has a structure in whichthe spacer layer 14 is sandwiched between the magnetic layers 13 and 15.By applying a voltage or passing a current from the wave detector 8 tothe continuous film 11, a change in magnetization, i.e., spin wave, canbe detected by the TMR effect (tunnel magnetoresistance effect) or GMReffect (giant magnetoresistance effect). Typically, the signal variationresulting from the spin wave is small. Hence, preferably, themagnetization directions of the two magnetic layers 13 and 15 are maderoughly orthogonal as in one of the structures shown in FIGS. 5A to 5Cto enhance the detection sensitivity. In particular, the magnetizationarrangement shown in FIG. 5B is preferable, because the magnetizationsof the magnetic layer 13 and 15 are both directed in the plane andsuitable to detect the in-plane variation of the magnetization directionof the magnetic layer 13.

FIG. 6 is a schematic view showing a partial cross section of the adderaccording to the embodiment.

On a substrate, not shown, continuous films 11 a and 11 b are providedvia an insulating film. An input section 5 a and a wave detector 8 a areconnected to the surface of the continuous film 11 a. The continuousfilm 11 a, the input section 5 a, and the wave detector 8 a constitutee.g. a computing unit 1. Furthermore, an input section 5 b and a wavedetector, not shown, are connected to the continuous film 11 b andconstitute a computing unit 2.

An input electrode 6 is connected to the input section 5 a. Anelectrical signal corresponding to e.g. the input A(0) or B(0) isapplied to the input electrode 6. As a result, a spin wave is excitedimmediately below the input section 5 a and propagated along thecontinuous film 11 a toward the wave detector 8 a. On the other hand, anoutput electrode 9 is connected to the wave detector 8 a. For instance,a bias voltage for producing the TMR effect is applied to the wavedetector 8 a. Thus, the spin wave propagated from the input section 5 ais detected as change in the voltage generated by the TMR effect, andoutputted as a voltage signal from the substrate side terminal 9 a ofthe output electrode 9.

Furthermore, the voltage signal outputted from the terminal 9 a isamplified in an amplifier 22 and inputted to a comparator 23. In thecomparator 23, the inputted voltage signal is compared with a thresholdvoltage Vth. For instance, if the voltage signal is larger than thethreshold voltage Vth, the comparator 23 outputs a corresponding voltagesignal.

The output of the comparator 23 is inputted to a terminal 6 a of theinput electrode 6 connected to the input section 5 b provided on thecontinuous film 11 b. That is, the output of the comparator 23corresponds to e.g. X(0) outputted from the computing unit 1, and isinputted to the input terminal 6 a of the computing unit 2.

The amplifier 22 and the comparator 23 can be placed on the same planeas the continuous films 11 a and 11 b, or placed above or below theinsulating film 21 shown in FIG. 6. For instance, as shown in FIG. 6,the amplifier 22 and the comparator 23 can be placed below thecontinuous film 11 to increase the packing density of computing units.Specifically, an integrated circuit including the amplifier 22 and thecomparator 23 is formed in the surface of a silicon substrate.Subsequently, the continuous film 11, the input section 5, the wavedetector 8 and the like are formed. Then, electrical connection can beconfigured as shown in FIG. 6.

FIGS. 7A and 7B are schematic diagrams showing examples of the voltagesignal outputted from the terminal 9 a of the output electrode 9 shownin FIG. 6. FIG. 7A shows a voltage waveform in the case where theamplitude of the spin wave detected in the wave detector 8 is relativelylarge. FIG. 7B shows a voltage waveform in the case where the amplitudeof the spin wave is relatively small. In general, in the TMR effect orGMR effect, the electrical resistance of the stacked film including twoor more magnetic layers changes with the relative angle between themagnetization directions of the magnetic layers. The amplitude of thespin wave is a temporal change in magnetization direction. Hence,depending on the magnitude of the amplitude of the spin wave propagatedin the magnetic layer 13, the relative angle between the magnetizationdirection of the magnetic layer 13 and the magnetization direction ofthe magnetic layer 15 changes. This changes the resistance of thecontinuous film 11 (see FIGS. 5A to 5C). Hence, a larger amplitude ofthe spin wave excited in the input section 5 a results in a largerresistance change of the continuous film 11 immediately below the wavedetector 8, and a larger change in the voltage outputted to the terminal9 a.

For instance, the voltage signal shown in FIGS. 7A and 7B is inputted tothe input terminal (IN) of the comparator 23 shown in FIG. 6. As athreshold voltage, Vth shown in FIGS. 7A and 7B is inputted to the inputterminal (REF) of the reference voltage. The comparator 23 can beconfigured so as to output a voltage corresponding to 1 if the magnitudeof the signal inputted to the input terminal (IN) exceeds Vth, and tooutput a voltage corresponding to 0 if the magnitude of the signalinputted to the input terminal (IN) does not exceed Vth. Thus, thecomparator 23 outputs a signal voltage corresponding to 1 only duringthe time when the signal voltage exceeds Vth as shown in FIG. 7A.

In the configuration shown in FIG. 6, the voltage signal outputted fromthe terminal 9 a of the output electrode 9 is amplified in the amplifier22. Alternatively, the voltage signal may be inputted directly to theinput terminal (IN) of the comparator 23 in the case where theresistance change detected in the wave detector 8 is sufficiently large.The comparator 23 and the amplifier 22 may be provided using theintegrated circuit technology.

Next, the arrangement of the input section 5 and the wave detector 8 inthe computing units 1 and 2 is described. If the magnetization directionof the magnetic layer 13 included in the continuous film 11 is madeperpendicular to the surface of the continuous film 11, the propagationcharacteristic of the spin wave is made isotropic (see FIG. 4C).Furthermore, the magnetic layer 13 made of a material with lowtransmission loss of the spin wave may ease restrictions to thearrangement of the input section 5 and the wave detector 8 and allowsvarious arrangements.

FIGS. 8A to 8D are schematic views showing arrangement examples of twoinput sections 5 and a wave detector 8 in the computing units 1 and 2.FIGS. 8A to 8C show arrangement examples of equal spacing d between thewave detector 8 and the input section 5. As shown in FIG. 8B, the wavedetector 8 and the input sections 5 may be placed on a straight line.Alternatively, as shown in FIGS. 8A and 8C, the input sections 5 may bearbitrarily arranged at positions with equal spacing from the wavedetector 8. In such arrangements, the time taken for spin wavesgenerated in the two input sections 5 to propagate in the continuousfilm 11 to the wave detector 8 is made equal. This is advantageous forsynchronization between the signals inputted to the two input sections5.

On the other hand, as shown in FIG. 8D, the diameter r of the inputsection 5 can be made twice or more the spacing d between the inputsection 5 and the wave detector 8. Then, the wavelength of the spin waveexcited in the input section 5 can be made longer than the spacing d.Thus, even if the spacing d between the input section 5 and the wavedetector 8 is different for the two input sections 5, the phasedifference between the spin waves reaching the wave detector 8 may bereduced.

As described above, the contact interface at which the input section 5and the continuous film 11 are electrically connected is preferablysmaller than a circle having a diameter of 200 nm. Hence, for instance,in the case where the input section 5 is entirely in contact with thecontinuous film, the diameter r of the input section is preferably setto 200 nm or less. On the other hand, the size of the wave detector 8can be designed irrespective of the size of the input section 5. Here,in order to maintain the detected spin wave at a uniform phase and toprevent attenuation of the output signal, the contact interface with thecontinuous film 11 is preferably made smaller. However, if the wavedetector 8 is made too small, the current density increases at thecontact interface with the continuous film 11. Then, a large spin torquemay occur during the detection operation and excite an unintended spinwave. Thus, to the extent of not exciting an unintended spin wave, thecontact interface of the wave detector 8 is preferably made smaller.Preferably, the size of the wave detector 8 is at least smaller than thewavelength of the detected spin wave. Since the half wavelength of thespin wave is almost the same as the diameter of the input section 5, thesize of the detector 8 is preferably smaller than twice the diameter ofthe input section.

FIGS. 9A to 9D are timing charts showing the relationship between thesignals A(0), B(0) inputted to the computing unit 1 or 2 and the outputsignal X(0). With time taken on the horizontal axis, the waveform ofeach signal is schematically shown. For instance, in the case where “1”is inputted, a pulse-like waveform is shown at the timing of input. Inthe case of “0”, the signal waveform is flat, and no pulse-like waveformis shown. (In the following, timing charts are shown likewise.)

In accordance with the waveform of the input signals A(0), B(0), for aperiod in which the signal value corresponds to “1”, a voltage V1 isapplied to the input section 5, or a current I1 is passed from the inputsection 5 to the continuous film 11. On the other hand, when the signalvalue is “0”, a voltage V0 is applied, or a current I0 is passed. Forinstance, setting V0=0 or I0=0 in the case of the signal value “0” ispreferable, because this facilitates distinction from the case of thesignal value “1”.

In FIG. 9A, the input signals A(0) and B(0) are each “1”. Hence, thevoltage V1 is applied to the input section 5 at a prescribed timing fora fixed time. For instance, in the computing units shown in FIG. 8A, 8B,or 8C, the spacing d between the input section 5 and the wave detector 8is equal for the two input sections 5. In this case, the timing forapplying the voltage V1 to the input section 5 for input of the signalA(0) and the input section 5 for input of the signal B(0) is preferablyset so that the phases of the excited spin waves are shifted by a halfwavelength. For instance, as shown in FIG. 9A, the timing for applyingthe voltage V1 to the input section 5 for input of the signal B(0) isset to be delayed by the time calculated by Equation (3):tr=(2f)⁻¹  (3)where f is the frequency of the spin wave.

Thus, when the spin waves generated in the two input sections 5 reachthe wave detector 8, their phases are shifted by a half wavelength. As aresult, the amplitude of the composite wave of the two spin waves isattenuated, and decreases the resistance change detected in the wavedetector 8. This decreases the voltage signal outputted from theterminal 9 a shown in FIG. 6, for instance. Thus, the output signal X0from the computing unit becomes “0”.

In FIG. 9B, the signal A(0) is “0”, and the signal B(0) is “1”. Hence,the input section 5 for input of the signal A(0) is applied with novoltage, and the input section 5 for input of the signal B(0) is appliedwith the voltage V1. In this case, no spin wave is excited in the inputsection 5 to which the signal A(0) has been inputted, but a spin wave isexcited only in the input section 5 to which the signal B(0) has beeninputted. Hence, no interference of spin waves occurs. Thus, the wavedetector 8 detects the spin wave excited in response to the input of thesignal B(0). Hence, the output signal X(0) becomes “1”.

In FIG. 9C, the signal A(0) is “1”, and the signal B(0) is “0”. Also inthis case, a spin wave is excited only in the input section 5 for inputof the signal A(0), and the output signal X(0) becomes “1”. In FIG. 9D,the signals A(0) and B(0) are both “0”. Thus, no spin wave is excited,and the output signal X(0) also becomes “0”.

FIGS. 10A to 10D are alternative timing charts showing the relationshipbetween the signals A(0), B(0) inputted to the computing unit 1 or 2 andthe output X(0).

In the spin wave-based computation, the duration of applying the voltageV1 or passing the current I1 to the input section 5 can be setarbitrarily to some extent. For instance, as shown in FIGS. 10A to 10D,in accordance with each waveform of the signals A(0) and B(0), the timefrom application (turn-on) to turn-off of the voltage V1 can beprolonged.

In FIG. 10A, the signals A(0) and B(0) are both “1”. The timing ofapplication of the voltage V1 to the input section 5 for input of thesignal A(0) and the timing of application of the voltage V1 to the inputsection 5 for input of the signal B(0) are shifted by tr. Furthermore,the durations tA and tB of application of the voltage V1 are made equal.Thus, the spin waves are attenuated by interference, and the outputsignal X(0) becomes “0”.

In FIG. 10B, the signal A(0) is “0”, and the signal B(0) is “1”. Theduration of application of the voltage V1 to the input section 5 forinput of the signal B(0) is tB. In this case, as shown in FIG. 10B, thevoltage V1 may be turned off after the wave detector 8 starts to detectthe output signal X(0).

In FIG. 10C, the signal A(0) is “1”, and the signal B(0) is “0”. Again,the duration of application of the voltage V1 to the input section 5 forinput of the signal A(0) is tA, and the voltage V1 may be turned offafter the wave detector 8 starts to detect the output signal X(0). InFIG. 10D, the signals A(0) and B(0) are both “0”. Thus, no spin wave isexcited, and the output signal X(0) also becomes “0”.

As shown in FIGS. 9A to 9D, by applying V1 with a pulse voltage of shortduration, the power consumption can be suppressed. As shown in FIGS. 10Ato 10D, by applying a voltage V1 of long duration, the duration of thewave is prolonged. This can improve the stability of the detection. Thisalso applies to the case of passing the current I1 to the input section5 in response to the signals A(0), B(0).

FIG. 11 is a plan view schematically showing an alternative arrangementexample of two input sections 5 and a wave detector 8 in the computingunits 1 and 2.

In the computing unit shown in FIG. 11, one of the spacings between thetwo input sections 5 and the wave detector 8 is made wider than theother by a half odd multiple of the wavelength λ of the spin wave. InFIG. 11, n represents an integer.

FIGS. 12A to 12D are timing charts showing the relationship between thesignals A(0), B(0) inputted to the computing unit shown in FIG. 11 andthe output X(0).

In FIG. 12A, the input signals A(0) and B(0) are both “1”. Thus, theinput section 5 for input of the signal A(0) and the input section 5 forinput of the signal B(0) are simultaneously applied with the voltage V1.One of the spacings between the two input sections 5 and the wavedetector 8 is longer than the other by a half odd multiple of thewavelength λ of the spin wave. Hence, two spin waves excited in therespective input sections 5 are out of phase by a half wavelength at thetime of reaching the wave detector 8. Thus, the amplitude of thecomposite wave of the two spin waves is attenuated, and decreases theoutputted voltage signal. Hence, as shown in FIG. 12A, the output signalX(0) becomes “0”.

In FIGS. 12B and 12C, one of the signals A(0) and B(0) is “0”, and theother is “1”. Hence, a spin wave is excited only in one of the two inputsections 5, and no interference occurs. The wave detector 8 detects thespin wave excited in one of the input sections 5, and the output signalX(0) becomes “1”. In FIG. 12D, the signals A(0) and B(0) are both “0”.Thus, no spin wave is excited, and the output signal X(0) also becomes“0”.

(Example of the Threshold Wave Computing Unit)

FIGS. 13A and 13B are schematic views showing arrangement examples ofthree input sections 5 and a wave detector 8 in the computing unit 3.The computing unit 3 is a threshold wave computing unit. Thecross-sectional structure of the input section 5, the wave detector 8,and the continuous film 11 can be the same as that in the computing unit1 or 2 serving as the wave computing unit.

In the example shown in FIG. 13A, the spacings d between the three inputsections 5 and the wave detector 8 are equal. Hence, three spin wavesexcited by the voltage or current simultaneously inputted to the threeinput sections 5 simultaneously reach the wave detector 8 without phasedifference. As a result, the wave detector 8 detects a composite wavehaving amplitude equal to the sum of the amplitudes of the spin waves.

Thus, for instance, the terminal 9 a (see FIG. 6) connected to the wavedetector 8 outputs a voltage signal with the magnitude corresponding tothe number of spin waves having reached the wave detector 8. Thisvoltage signal can be compared with a prescribed threshold voltage torealize the function of a threshold computing unit for e.g. outputting“1” if the number of spin waves, or signals “1”, is equal to or largerthan a prescribed number, and outputting “0” if the number falls belowthe prescribed number. Specifically, a threshold voltage is inputted tothe REF terminal of the comparator 23 of FIG. 6 to cause it to outputthe result of comparison with the signal voltage.

In the example shown in FIG. 13B, the diameter r of the three inputsections 5 is made relatively large so that the wavelength of theexcited spin wave becomes longer than the spacing d between the inputsection 5 and the wave detector 8. That is, the spacing d can be madesmaller than twice the diameter r. This can decrease the phasedifference occurring when the spin waves simultaneously excited in thethree input sections 5 reach the wave detector 8. As a result, themagnitude of the amplitude of the composite wave detected in the wavedetector 8 corresponds to the number of spin waves excited in the threeinput sections 5. This enables the function of a threshold computingunit.

FIGS. 14A to 15D are timing charts showing the relationship between thesignals A(0), B(0), C(−1) inputted to the computing unit 3 and theoutput C(0). The computing unit 3 is a threshold computing unit. Thecomputing unit 3 outputs “1” as the output C(0) if the number of signals“1” inputted is two or more, and outputs “0” as the output C(0) if thenumber of signals “1” inputted is one or less.

In FIG. 14A, the input signals A(0), B(0), and C(−1) are all “1”. Thus,the input section 5 for input of the signal A(0), the input section 5for input of the signal B(0), and the input section 5 for input of thesignal C(−1) are simultaneously applied with the voltage V1. Forinstance, in the case of the computing unit according to the arrangementexample of FIG. 13A, three spin waves excited in the respective inputsections 5 reach the wave detector 8 and are combined. The wave detector8 detects a composite wave having amplitude of three times that of thespin wave excited in the input section 5. Thus, “1” is outputted as theoutput C(0).

In FIGS. 14B, 14C, and 14D, two of the input signals A(0), B(0), andC(−1) are “1”, and the remaining one signal is “0”. Hence, a spin waveis excited in two of the three input sections 5. The wave detector 8detects a composite wave of two spin waves, and “1” is outputted as theoutput C(0).

In FIGS. 15A, 15B, and 15C, one of the input signals A(0), B(0), andC(−1) is “1”, and the remaining two signals are “0”. Hence, a spin waveis excited in one of the three input sections 5. The wave detector 8detects the excited spin wave. However, the outputted voltage signal islower than the threshold voltage. Hence, “0” is outputted as the outputC(0). In FIG. 15D, the signals A(0), B(0), and C(−1) are all “0”. Thus,no spin wave is excited, and the output C(0) also outputs “0”.

(Variation 1)

FIGS. 16A to 16D are partial sectional views schematically showing theinput section 5 and the continuous film of a computing unit according toa variation of the first embodiment. In the configuration of thecomputing unit according to this variation, a section for imparting anexternal magnetic field, such as a permanent magnet or wiring magnet, isprovided around the continuous film 11 so as to act on the magnetizationof the magnetic layer 13.

The configuration of the external magnetic field acting on themagnetization of the magnetic layer 13 can be configured so that themagnetization direction M2 due to spin torque generated by the signal ofthe voltage or current applied to the input section 5 competes with themagnetization direction H0 due to the external magnetic field. Then, astable oscillation state of the spin wave can be obtained, and the spinwave can be efficiently generated. For instance, in the configurationshown in FIGS. 16A and 16B, the magnetization direction M1 of themagnetic layer 15 magnetized parallel to the surface of the continuousfilm 11 is opposite to the direction H0 of the external magnetic field.The angle therebetween is close to 180 degrees. In this case, a currentJ1 passed from the input section 5 via the magnetic layer 13 toward themagnetic layer 15 causes an action of spin torque for magnetizing themagnetic layer 13 in the same direction M1 as the magnetic layer 15. Onthe other hand, the external magnetic field has the action of causingmagnetization in the direction H0 opposite to the magnetic layer 15. Asa result, these actions compete with each other and can easily excite aspin wave.

On the other hand, in the configuration shown in FIGS. 16C and 16D, thedirection H0 of the external magnetic field is matched with themagnetization direction M1 of the magnetic layer 15. In this case, acurrent J2 passed from the magnetic layer 15 via the magnetic layer 13toward the input section 5 causes an action of spin torque formagnetizing the magnetic layer 13 in the direction M2 opposite to themagnetization direction M1 of the magnetic layer 15. As a result, theaction of the external magnetic field competes with the action of spintorque. This can facilitate excitation of a spin wave.

FIG. 17 is a schematic view showing a cross section of the computingunit according to this variation equipped with an external magneticfield imparting section 18.

On a substrate, not shown, a continuous film 11 is provided via aninsulating film 21. An input section 5 and a wave detector 8 areconnected to the surface of the continuous film 11. The input section 5is connected to an input electrode 6, and the wave detector 8 isconnected to an output electrode 9. Furthermore, an external magneticfield imparting section 18 is provided above the continuous film 11 viathe insulating film 21. The external magnetic field imparting section 18may be a permanent magnet. Alternatively, the external magnetic fieldimparting section 18 may be formed as a metal wiring extending in thedepth direction of the figure so that the magnetic field generated bypassing a current in the metal wiring acts on the continuous film 11.

(Variation 2)

FIGS. 18A to 18C are partial sectional views schematically showing theinput section 5 and the continuous film 11 of a computing unit accordingto a second variation of the first embodiment. In this variation, thenumber of magnetic layers included in the continuous film 11 is one.

In FIG. 18A, a magnetic layer 25 is formed on a substrate not shown. Aninput section 5 formed from a non-magnetic conductive material isconnected to the magnetic layer 25. The continuous film 11 is themagnetic layer 25 itself. The magnetization direction M3 of the magneticlayer 25 is made perpendicular to the surface of the magnetic layer 25.

Thus, even in the case of one magnetic layer, portions having differentmagnetic anisotropy are locally induced due to the forming of the inputsection 5. Hence, by applying a voltage to the input section 5 orpassing a current in the magnetic layer 25 via the input section 5, spintorque occurs and excites a spin wave. Furthermore, because themagnetization direction M3 is perpendicular to the surface of themagnetic layer 25, the spin wave has the isotropic propagationcharacteristic in the magnetic layer 25.

Alternatively, as shown in FIG. 18B, the magnetization direction M3 ofthe magnetic layer 25 can be made parallel to the surface of themagnetic layer 25. In this case, preferably, an antiferromagnetic layer16 is provided on the side opposite to the surface provided with theinput section 5 to pin the magnetization direction M3 in the magneticlayer 25. This can prevent generation of a spin wave in the continuousfilm 25 due to factors other than the input signal. Thus, it is alsoadvantageous that the magnetic layer can be easily manufactured with themagnetization direction parallel to the surface.

Furthermore, on the surface of the magnetic layer 25, a conductiveprotective film, not shown, may be formed as a cap layer. Alternatively,as shown in FIG. 18C, an insulating layer 26 may be provided between themagnetic layer 25 and the input section 5.

FIGS. 19A and 19B are schematic views showing a cross section (FIG. 19A)and a plan view (FIG. 19B) of the computing unit according to the secondvariation. As shown in FIG. 19A, the computing unit according to thisvariation includes an input section 5 connected to the continuous film11, an input electrode 6, and a wave detector 28 provided via aninsulating film 21.

As shown in FIG. 19B, the wave detector 28 is made of coplanar lines 28a and 28 b formed in parallel. The wave detector 28 detects the changeof the magnetic field due to the spin wave propagated in the continuousfilm 11 by the electromagnetic induction effect. More specifically, thespin wave excited in the input section 5 by the signal inputted from theinput electrode 6 is propagated in the continuous film 11. The wavedetector 28 can detect and output the change of the magnetic field dueto the spin wave as a radio frequency induced current. Here, instead ofthe coplanar lines, various waveguides such as microstrip lines can beused.

(Variation 3)

FIGS. 20A and 20B are schematic views showing a partial cross section ofthe input section 7 (FIG. 20A) and a partial cross section of the wavedetector 8 (FIG. 20B) according to a third variation.

As shown in FIG. 20A, the input section 7 is also formed from aconductive magnetic body. Furthermore, a spacer layer 14 is providedbetween the input section 7 and the magnetic layer 25. Also in such astructure, a spin wave can be excited by applying a voltage to the inputsection 7 or passing a current in the magnetic layer 25 from the inputsection 7 via the spacer layer 14. Here, in order to excite a spin wavewith lower energy, the magnetization direction M5 of the input section 7and the magnetization direction M4 of the magnetic layer 25 arepreferably orthogonal.

On the other hand, the wave detector for detecting the spin wavepropagated in the magnetic layer 25 can be made of coplanar lines 28 aand 28 b shown in FIG. 19B. Furthermore, as shown in FIG. 20B, the wavedetector 8 can be provided on the surface of a layer structure in whichthe magnetic layer 25, the spacer layer 14, and a magnetic layer 27 arestacked. By the configuration shown in FIG. 20B, the spin wave can bedetected using the TMR effect or GMR effect.

(Variation 4)

FIG. 21 is a schematic view showing a partial cross section of thecomputing units 1 and 2 according to a fourth variation.

In this variation, the voltage signal outputted from the terminal 9 a ofthe computing unit 1 is inputted to the input terminal 6 a of thecomputing unit 2 via a low pass filter 32. Furthermore, a diode 31 forrectification is placed between the terminal 9 a and the low pass filter32. Thus, the voltage signal outputted from the computing unit 1 can beconverted to a unipolar signal and inputted to the computing unit 2.Here, depending on the waveform of the electrical signal outputted fromthe computing unit 1, it is possible to provide an embodiment withoutthe low pass filter 32.

(Variation 5)

FIG. 22 is a perspective view schematically showing a computing unitaccording to a fifth variation. Also in the computing unit according tothis variation, two input sections 5 and a wave detector 8 made of anon-magnetic conductive material are provided on a continuous film 11.The continuous film 11 is configured in a layer structure of a magneticlayer 13, a spacer layer 14, and a magnetic layer 15 from the surface.The wave detector 8 in this variation is provided as a wiring made of anon-magnetic conductive material as shown in FIG. 22.

If a spin wave is excited in the magnetic layer 13, a spin currentcorresponding to the magnitude of its amplitude flows into the wiringprovided as the wave detector 8. Then, in the wiring made of anon-magnetic body, by the effect of spin-orbit interaction, a currentcorresponding to the magnitude of the spin current flows in the wiring.Such a phenomenon is called the inverse spin Hall effect. As a result,the magnitude of the amplitude of the spin wave can be converted to themagnitude of the current flowing in the wiring and detected.

Here, in order to increase the detection sensitivity, the non-magneticconductive material used for the wiring is preferably a materialcontaining substances with high spin-orbit interaction. Specifically,substances having an atomic number of 37 or more are preferable becauseof high spin-orbit interaction. For instance, platinum Pt, gold Au, oran alloy containing one of them can be used.

The computing unit shown in FIG. 22 is a wave computing unit having theconfiguration of the computing unit 1 or 2. Here, the wave computingunit 8 according to this example can be used also for the threshold wavecomputing unit having the configuration of the computing unit 3.

(Variation 6)

FIGS. 23A and 23B are schematic views showing a computing unit 3according to a sixth variation. FIG. 23A shows a front view, and FIG.23B shows a plan view. In this variation, a continuous film 34 isprovided on a substrate, not shown. Three input sections 35 and a wavedetector 38 are provided on the continuous film 34. The continuous film34 includes a surface layer made of a piezoelectric body.

The input section 35 includes an electrode pair composed of a firstelectrode 35 a and a second electrode 35 b. A pulse voltage oralternating voltage corresponding to the input signal is applied betweenthe first electrode 35 a and the second electrode 35 b. Then, thesurface of the piezoelectric body is strained to generate a surfaceacoustic (elastic) wave. The surface acoustic wave has a wavelengthcorresponding to the spacing between the first electrode 35 a and thesecond electrode 35 b. The surface acoustic wave is propagated along thesurface of the continuous film 34.

Here, the propagation characteristic of the surface acoustic wavedepends on the crystallinity of the piezoelectric body. The surfaceacoustic wave is propagated in a direction corresponding to the crystalorientation. In particular, in a single crystal piezoelectric body, auniform surface acoustic wave is excited. Hence, the continuous film 34or the surface layer of the continuous film 34 is preferably formed froma single crystal piezoelectric body.

Furthermore, in order to equalize the wavelength of the surface acousticwave excited in each input section 35, for instance, it is preferablethat the same electrode shape be used in the input sections 35 with anequal spacing between the first electrode 35 a and the second electrode35 b.

On the other hand, as shown in FIG. 23B, the wave detector 38 providedon the continuous film 34 is configured so that two electrodes 38 a and38 b formed in a comb shape are meshed with each other. The surfaceacoustic waves excited in the respective input sections 35 andpropagated at the surface of the continuous film 34 are combined at theposition of the wave detector 38. Then, in the wave detector 38, anelectrical signal corresponding to the amplitude of the composite wavecan be extracted by the piezoelectric effect.

Here, preferably, the longer side of the linearly formed electrodes 38 aand 38 b is arranged perpendicular to the direction of the input section35. That is, by arrangement orthogonal to the propagation direction ofthe surface acoustic wave directed from the input section 35 to the wavedetector 38, the detection efficiency of the surface acoustic wave canbe increased. Furthermore, preferably, the direction from the inputsection 35 toward the wave detector (the horizontal direction in FIGS.23A and 23B) is aligned with the crystal direction maximizing thepropagation speed of the surface acoustic wave.

Furthermore, the spacing between the first electrode 35 a and the secondelectrode 35 b is matched with the spacing between the comb-shapedelectrodes 38 a and 38 b of the wave detector 38. This makes it possibleto detect only the elastic wave excited in the input section 35.

In the computing unit shown in FIGS. 23A and 23B, the distance from theinput sections 35 to the wave detector 38 is fixed. By aligning thetiming of applying a voltage to the input sections 35, the phases of thesurface acoustic waves combined at the position of the wave detector 38can be aligned. This enables the function of a threshold wave computingunit.

Alternatively, two input sections 35 can be provided on the continuousfilm 34, and the distances from the respective input sections 35 to thewave detector 38 (combining position) can be shifted by a halfwavelength of the surface acoustic wave. Thus, the combined surfaceacoustic waves can be set in opposite phase. This also enables thefunction of a wave computing unit for performing exclusive OR operation.

As a method for inverting the phase of the surface acoustic wavecombined at the position of the wave detector 38, it is also possible touse the method of shifting the timing of applying a voltage to the inputsection 35 by the propagation time of a half wavelength. Alternatively,it is also possible to use the method of inverting the polarity of thevoltage applied to the first electrode 35 a and the second electrode 35b in one of the input sections 35.

Second Embodiment

FIG. 24 is a block diagram showing an adder according to a secondembodiment. The adder according to the embodiment is an (m+1)-bit adder40. In response to input of signals corresponding to signals A(0) toA(m), signals B(0) to B(m), and a signal C(−1), the adder outputscomputation results S(0) to S(m), and C(m). The signals A(0) to A(m)correspond to the bit values of the i-th to (i+m)-th positions of abinary value A. The signals B(0) to B(m) correspond to the bit values ofthe i-th to (i+m)-th positions of a binary value B. The signal C(−1)corresponds to the carry bit value from the (i−1)-th position to thei-th position for the sum of the binary value A and the binary value B.Here, m is an integer of 0 or more.

A(0) to A(m), B(0) to B(m), and C(−1) are one of the two inputsrepresented by “0” or “1”. The input terminal of the adder receivesinput of an electrical signal corresponding to “0” or “1”. On the otherhand, the output terminal outputs a signal corresponding to S(0) toS(m), and C(m), which are likewise either “0” or “1”.

As shown in FIG. 24, the (m+1)-bit adder 40 can be regarded as an adderincluding an m-bit adder 41, a computing unit 3 m+1, a computing unit 3m+2, and a computing unit 3 m+3.

Furthermore, the m-bit adder 41 includes an (m−1)-bit adder, a computingunit 3 m−2, a computing unit 3 m−1, and a computing unit 3 m. Inresponse to input of A(0) to A(m−1), B(0) to B(m−1), and C(−1), them-bit adder 41 outputs S(0) to S(m−1), and C(m−1).

Moreover, the (m−1)-bit adder is regarded as an adder including an(m−2)-bit adder, a computing unit 3 m−5, a computing unit 3 m−4, and acomputing unit 3 m−3. In response to input of A(0) to A(m−2), B(0) toB(m−2), and C(−1), the (m−1)-bit adder outputs S(0) to S(m−2), andC(m−2).

On the other hand, for m=0, the adder 40 is the 1-bit adder shown inFIG. 1, and includes a computing unit 1, a computing unit 2, and acomputing unit 3. In response to input of A(0), B(0), and C(−1), theadder 40 outputs S(0) and C(0).

Ultimately, the (m+1)-bit adder 40 includes computing units 1 to 3 m+3.Among them, the computing unit 3 k+1 is a first wave computing unit. Inresponse to input of A(k) and B(k), the computing unit 3 k+1 outputs anintermediate output X(k). Here, k is an integer of 0 to m. TABLE 5 showsthe truth values of the computing unit 3 k+1. The computing unit 3 k+2is a second wave computing unit. In response to input of X(k) andC(k−1), the computing unit 3 k+2 outputs a computation result S(k).TABLE 6 shows the truth values of the computing unit 3 k+2.

TABLE 5 A[k] B[k] X[k] 0 0 0 1 0 1 0 1 1 1 1 0

TABLE 6 X[k] C[k − 1] S[k] 0 0 0 1 0 1 0 1 1 1 1 0

The truth table shown in TABLE 7 joins TABLES 5 and 6 and shows thecomputation result S(k) in response to inputs A(k), B(k), and C(k−1). Asis clear from TABLE 7, the computation result S(k) does not change evenif the inputs A(k), B(k), and C(k−1) are interchanged. For instance,TABLE 7 indicates that the computation result S(k) remains unchanged asdescribed above even in the configuration in which A(k) and C(k−1) areinputted to the first wave computing unit, and X(k) and B(k) areinputted to the second wave computing unit.

TABLE 7 A[k] B[k] C[k − 1] C[k] 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 0 1 01 0 1 1 0 1 1 1 1 1 1 1

Furthermore, the computing unit 3 k+3 is a threshold wave computingunit. In response to input of A(0) to A(k), B(0) to B(k), and C(−1), thecomputing unit 3 k+3 outputs C(k). Furthermore, in accordance withEquation 1, the computing unit 3 k+3 outputs a signal corresponding to“0” or “1” with reference to a threshold corresponding to 2 k+1.

Here, each input signal is weighted. With the weight of the input signalA(0) set to 1, weighting is performed so that the weight of the inputsignal A(i) (i is an integer of 0 to k) is multiplied by 2i.Specifically, for instance, weighting can be performed by providing 2iinput electrodes, each producing a signal A(i).

Alternatively, weighting can be performed also by applying a voltage orcurrent to the input section so that the magnitude of the input signalA(i) is 2i times the magnitude of the input signal A(0). Thus, themagnitude of the amplitude of the excited wave is weighted. As a result,the threshold logic operation represented in Equation 1 is performed.

$\begin{matrix}{C_{m} = \left\{ \begin{matrix}1 & {{{{if}\mspace{14mu}{\sum\limits_{i = 0}^{m}\;{2^{i}A_{i}}}} + {\sum\limits_{i = 0}^{m}{2^{i}B_{i}}} + C_{- 1}} \geq 2^{m + 1}} \\0 & {{{{if}\mspace{14mu}{\sum\limits_{i = 0}^{m}\;{2^{i}A_{i}}}} + {\sum\limits_{i = 0}^{m}{2^{i}B_{i}}} + C_{- 1}} \leq {2^{m + 1} - 1}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

The first wave computing unit, the second wave computing unit, and thethreshold wave computing unit can be configured similarly to the wavecomputing unit and the threshold wave computing unit, respectively,described in the first embodiment.

FIG. 25 is a block diagram showing a 2-bit adder 42 for m=1. The 2-bitadder 42 includes computing units 51 to 56. In response to input ofA(0), B(0), A(1), B(1), and C(−1), the 2-bit adder 42 outputs S(0),S(1), and C(1). The computing unit 51 and the computing unit 54 arefirst wave computing units, and output intermediate outputs X(0) andX(1), respectively. The computing unit 52 and the computing unit 55 aresecond wave computing units. In response to input of X(0) and C(−1), andX(1) and C(0), the computing unit 52 and the computing unit 55 outputS(0) and S(1). Furthermore, the computing units 53 and 56 are thresholdwave computing units. In response to input of A(0), B(0), and C(−1), thecomputing unit 53 outputs C(0). In response to input of A(0), B(0),A(1), B(1), and C(−1), the computing unit 56 outputs C(1).

FIGS. 26A to 26C are plan views schematically showing the configurationof the computing unit 56 in the 2-bit adder shown in FIG. 25. Thecomputing unit 56 performs a threshold logic operation in accordancewith Equation 2. More specifically, in response to input of A(0), B(0),C(−1), and two A(1) and two B(1), the computing unit 56 outputs C(1).That is, the computing unit 56 is a 7-input 1-output computing unit. Asshown in FIGS. 26A to 26C, the computing unit 56 includes seven inputsections 5 and one wave detector 8. The spin waves excited in therespective input sections 5 are combined at the position of the wavedetector 8, which outputs a signal corresponding to the composite wave.Here, if the signal intensity detected in the wave detector 8 is higherthan the level corresponding to threshold 4, a computation resultcorresponding to “1” is outputted in accordance with Equation 2. If thesignal level falls below threshold 4, a computation result correspondingto “0” is outputted.

$\begin{matrix}{C_{m} = \left\{ \begin{matrix}1 & {{{{if}\mspace{14mu} 2\; A_{1}} + {2\; B_{1}} + A_{0} + B_{0} + C_{- 1}} \geq 4} \\0 & {{{{if}\mspace{14mu} 2\; A_{1}} + {2\; B_{1}} + A_{0} + B_{0} + C_{- 1}} \leq 3}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

As described above, the spacing between the input section 5 and the wavedetector 8 can be narrower than the wavelength of the spin wave.Furthermore, the propagation characteristic of the spin wave can beisotropic, and the propagation loss can be low. Then, the input sections7 and the wave detector 8 can be arbitrarily arranged as shown in FIGS.26A and 26B. Alternatively, as shown in FIG. 26C, the input sections 5may be arranged at equal distances around the wave detector 8.

Third Embodiment

FIG. 27 is a block diagram showing an m-bit adder 44 according to athird embodiment. The adder 44 according to this embodiment includes qsub-adders (q is an integer of 1 or more). For instance, FIG. 27 showsan example for q=2, including a sub-adder 45 and a sub-adder 46.

The sub-adder according to this embodiment includes first to n-thaddition computing units and a carry computing unit. In response toinput of signals corresponding to the bit values A[j] to A[j+n−1] andB[j] to B[j+n−1] of the j-th to (j+n−1)-th positions of binary values Aand B, and a carry bit value C[j−1], the first to n-th additioncomputing units output computation results S(j) to S(j+n−1), and thecarry computing unit outputs a computation result C(j+n−1) correspondingto the carry bit value C[j+n−1]. Here, j and n are integers, and i≦j,j+n≦i+m.

The first addition computing unit inputs signals corresponding to two ofA[j], B[j], and C[j−1] to the first wave computing unit and causes it tooutput X(j). Furthermore, the first addition computing unit inputs asignal corresponding to the remaining one of A[j], B[j], and C[j−1] notinputted to the first wave computing unit, and X(j) to the second wavecomputing unit and causes it to output the S(j).

The p-th adder (p is an integer of 1 to n) inputs A(j) to A(j+p−2), B(j)to B(j+p−2), and C(j−1) to the threshold wave computing unit and causesit to output C(j+p−2). Furthermore, the p-th adder inputs A(j+p−1) andB(j+p−1) to the first wave computing unit and causes it to outputX(j+p−1). Furthermore, the p-th adder inputs C(j+p−2) and X(j+p−1) tothe second wave computing unit and causes it to output S(j+p−1).

Furthermore, the carry computing unit inputs A(j) to A(j+n−1), B(j) toB(j+n−1), and C(j−1) to the threshold wave computing unit and causes itto output C(i+n−1).

The sub-adder 45 shown in FIG. 27 is an n-bit sub-adder. In response toinput of A(j) to A(j+n−1), B(j) to B(j+n−1), and C(j−1), the sub-adder45 outputs S(j) to S(j+n−1), and C(j+n−1). The sub-adder 46 is a w-bitsub-adder. In response to input of A(j+n) to A(j+n+w−1), B(j+n) toB(j+n+w−1), and C(j+n−1), the sub-adder 46 outputs S(j+n) to S(j+n+w−1),and C(j+n+w−1). Here, w is an integer of 1 or more, and n+w=m.

For instance, for n=4 and w=4, the sub-adders 45 and 46 are 4-bitsub-adders. Then, the adder 44 can be regarded as an 8-bit adder. Inresponse to input of A(0) to A(7), B(0) to B(7), and C(−1), the adder 44outputs S(0) to S(7), and C(7).

FIG. 28 is a block diagram showing the configuration of a 4-bitsub-adder 45 a. The 4-bit sub-adder 45 a includes computing units 51 to62. In response to input of A(0) to A(3), B(0) to B(3), and C(−1), the4-bit sub-adder 45 a outputs S(0) to S(3), and C(3). The computing unit51, the computing unit 54, the computing unit 57, and the computing unit60 are first wave computing units. The computing unit 52, the computingunit 55, the computing unit 58, and the computing unit 61 are secondwave computing units. The computing unit 53, the computing unit 56, thecomputing unit 59, and the computing unit 62 are threshold wavecomputing units.

The first addition computing unit is composed of the computing unit 51and the computing unit 52. The computing unit 51 receives input of A(0)and B(0), and outputs X(0). The computing unit 52 receives input ofC(−1) and X(0), and outputs S(0). As shown in FIG. 2, even if the inputsB(0) and C(−1) are interchanged, the output S(0) does not change.

The second addition computing unit is composed of the computing unit 53,the computing unit 54, and the computing unit 55. The computing unit 53receives input of A(0), B(0), and C(−1), and outputs C(0). The computingunit 54 receives input of A(1) and B(1), and outputs X(1). The computingunit 55 receives input of C(0) and X(1), and outputs S(1). Furthermore,the third addition computing unit is composed of the computing unit 56,the computing unit 57, and the computing unit 58. The fourth additioncomputing unit is composed of the computing unit 59, the computing unit60, and the computing unit 61.

On the other hand, the computing unit 62 is a carry computing unit. Thecomputing unit 62 receives input of A(0) to A(3), B(0) to B(3), andC(−1), and outputs C(3).

Furthermore, the adder 44 can be configured as a 16-bit adder includingfour 4-bit sub-adders. Alternatively, the adder 44 can be configured asa 16-bit adder including two 8-bit sub-adders. Here, the number of bitsof the sub-adders 45 and 46 can be increased by adding an additioncomputing unit by the same rule as the 4-bit sub-adder 45 a. As analternative configuration, the sub-adder may be regarded as the adder44, which may further include a sub-adder.

The invention has been described above with reference to the first tothird embodiments. However, the invention is not limited to theseembodiments.

For instance, any configurations for specific dimensions and materialsof the components constituting the continuous film, and the shape andmaterial of e.g. the electrode, protective film, and insulating film areencompassed within the scope of the invention as long as those skilledin the art can practice the invention and achieve similar effects bysuitably selecting such configurations based on the state of the art atthe time of filing of this application.

Furthermore, in the first to third embodiments, for instance, theconfiguration shown in the figure can be turned upside down. Thecomponents such as the antiferromagnetic layer, intermediate layer, andinsulating layer in the continuous film may be configured as a singlelayer, or may have a structure in which two or more layers are stacked.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. Indeed, the novel embodiments described hereinmay be embodied in a variety of other forms; furthermore, variousomissions, substitutions and changes in the form of the embodimentsdescribed herein may be made without departing from the spirit of theinventions. The accompanying claims and their equivalents are intendedto cover such forms or modifications as would fall within the scope andspirit of the invention.

What is claimed is:
 1. An adder comprising: a first wave computing unitincluding: a pair of first input sections receiving signalscorresponding to two bit values selected from A[i+k−1], B[i+k−1] andC[i+k−2], the A[i+k−1] being the bit value of the (i+k−1)-th position ofa binary value A, the B[i+k−1] being the bit value of the (i+k−1)-thposition of the binary value B, and the C[i+k−2] being a carry bit valuefrom the (i+k−2)-th position to the (i+k−1)-th position resulting fromaddition of the binary value A and the binary value B (i and k beingintegers); a first wave transmission medium having a continuous filmincluding a magnetic body connected to the first input sections; and afirst wave detector outputting X(k−1) as a result of computation by spinwaves induced in the first wave transmission medium by the signalscorresponding to the two bit values; a second wave computing unitincluding: a pair of second input sections receiving a signalcorresponding to the bit value not selected as the input to the firstinput sections among the A[i+k−1], B[i+k−1] and C[i+k−2], and the outputX(k−1); a second wave transmission medium having a continuous filmincluding a magnetic body connected to the second input sections; and asecond wave detector outputting S(k−1) as a result of computation byspin waves induced in the second wave transmission medium by the signalcorresponding to the bit value not selected and the output X(k−1); and athreshold wave computing unit including: a plurality of third inputsections receiving signals corresponding to the A[i] to A[i+k−1], theB[i] to B[i+k−1], and the carry bit value C[i−1]; a third wavetransmission medium having a continuous film including a magnetic bodyconnected to the third input sections; and a third wave detectoroutputting C(k−1) as a result of computation by spin waves induced inthe third wave transmission medium by the signals corresponding to theA[i] to A[i+k−1], B[i] to B[i+k−1], and C[i−1].
 2. The adder accordingto claim 1, further comprising: a sub-adder including: first to n-thaddition computing units outputting the computation results S(j) toS(j+n−1) in response to the signals corresponding to the bit values A[j]to A[j+n−1] of the j-th to (j+n−1)-th positions of the binary value A (jand n being integers, i≦j), the bit values B[j] to B[j+n−1] of the j-thto (j+n−1)-th positions of the binary value B, and the carry bit valueC[j−1]; and a carry computing unit outputting a computation resultC(j+n−1) corresponding to the carry bit value C[j+n−1], wherein thefirst addition computing unit is configured: to input signalscorresponding to two of the A[j], B[j], and C[j−1] to the first wavecomputing unit and causing the first wave computing unit to output theX(j); and to input a signal corresponding to the remaining one of theA[j], B[j], and C[j−1] not inputted to the first wave computing unit,and the X(j) to the second wave computing unit and causing the secondwave computing unit to output the S(j), the p-th addition computing unit(p being an integer, 1<p≦n) is configured: to input signalscorresponding to the A[j] to A[j+p−2], the B[j] to B[j+p−2], and theC[j−1] to the threshold wave computing unit and causing the thresholdwave computing unit to output the C(j+p−2); to input signalscorresponding to the A[j+p−1] and the B[j+p−1] to the first wavecomputing unit and causing the first wave computing unit to output theX(j+p−1); and to input signals corresponding to the C(j+p−2) and theX(j+p−1) to the second wave computing unit and causing the second wavecomputing unit to output the S(j+p−1), and the carry computing unit isconfigured: to input signals corresponding to the A[j] to A[j+p−1], B[j]to B[j+p−1], and the C[j−1] to the threshold wave computing unit andcausing the threshold wave computing unit to output the C(j+p−1).
 3. Theadder according to claim 1, wherein spacings from the input sections tothe wave detector are equal in at least one of the first computing unitand the second computing unit.
 4. The adder according to claim 1,wherein difference of spacings from the plurality of the input sectionsto the wave detector is equal to an odd multiple of a half wavelength ofa wave induced in the wave transmission medium in at least one of thefirst computing unit and the second computing unit.
 5. The adderaccording to claim 1, wherein spacings from the plurality of the inputsections to the wave detector are narrower than twice a diameter of theinput section in at least one of the first computing unit, the secondcomputing unit and the threshold wave computing unit.
 6. The adderaccording to claim 1, wherein at least one of the first wave computingunit, the second wave computing unit, and the threshold wave computingunit includes a detector configured to output a result of comparing asignal corresponding to a local amplitude of the spin wave induced inthe wave transmission medium with a prescribed threshold.
 7. The adderaccording to claim 6, wherein at least one of the first wave computingunit, the second wave computing unit, and the threshold wave computingunit includes an amplifier configured to amplify the signalcorresponding to the local amplitude of the spin wave induced in thewave transmission medium.
 8. The adder according to claim 1, wherein atleast one of the first wave computing unit, the second wave computingunit, and the threshold wave computing unit includes a rectifierconfigured to rectify a signal corresponding to a local amplitude of thewave induced in the wave transmission medium.
 9. The adder according toclaim 1, wherein each of the first input section, the second inputsection and the third input section is connected to the wavetransmission medium via a region smaller than a circle having a diameterof 200 nm.
 10. The adder according to claim 1, wherein each of the firstwave computing unit, the second wave computing unit, and the thresholdwave computing unit includes an external magnetic field impartingsection configured to impart an external magnetic field applied to thewave transmission medium.
 11. The adder according to claim 10, whereinat least one of the first wave transmission medium, the second wavetransmission medium and the third wave transmission medium includes twomagnetic layers and a spacer layer provided therebetween, whereinmagnetic fields of the two magnetic layers cross each other at an anglebetween 60 degrees and 120 degrees.
 12. The adder according to claim 10,wherein the magnetization of the magnetic layer in which the spin waveis propagated is perpendicular to a surface of the continuous film. 13.The adder according to claim 1, wherein at least one of the first wavedetector, the second wave detector and the third wave detector includescoplanar lines.
 14. The adder according to claim 1, wherein at least oneof the first wave detector, the second wave detector and the third wavedetector includes a wiring made of a non-magnetic conductive material.15. The adder according to claim 1, wherein the first wave detector, thesecond wave detector and the third wave detector have a size smallerthan twice a diameter of the input section in each of the firstcomputing unit, the second computing unit and the threshold wavecomputing unit.
 16. The adder according to claim 1, wherein the firstwave computing unit and the second wave computing unit perform exclusiveOR operation.
 17. The adder according to claim 1, wherein the third wavecomputing unit performs a threshold computation based on an outputcorresponding to number of spin waves induced by a plurality of signalsat the third input sections.
 18. An adder comprising: a first wavecomputing unit including: a pair of first input sections receivingsignals corresponding to two bit values selected from A[i+k−1], B[i+k−1]and C[i+k−2], the A[i+k−1] being the bit value of the (i+k−1)-thposition of a binary value A, the B[i+k−1] being the bit value of the(i+k−1)-th position of a binary value B, and the C[i+k−2] being a carrybit value from the (i+k−2)-th position to the (i+k−1)-th positionresulting from addition of the binary value A and the binary value B (iand k being an integer); a first wave transmission medium having acontinuous film including a piezoelectric body connected to the firstinput sections; and a first wave detector configured to output X(k−1) asa result of computation by elastic waves induced in the first wavetransmission medium by the signals corresponding to the two bit values;a second wave computing unit including: a pair of second input sectionsreceiving a signal corresponding to the bit value not selected as theinput to the first input section among the A[i+k−1], B[i+k−1] andC[i+k−2], and the output X(k−1); a second wave transmission mediumhaving a continuous film including a piezoelectric body connected to thesecond input sections; and a second wave detector outputting S(k−1) as aresult of computation by elastic waves induced in the second wavetransmission medium by the signal corresponding to the bit value notselected and the output X(k−1); and a threshold wave computing unitincluding: a plurality of third input sections receiving signalscorresponding to the A[i] to A[i+k−1], the B[i] to B[i+k−1], and thecarry bit value C[i−1]; a third wave transmission medium having acontinuous film including a piezoelectric body connected to the thirdinput sections; and a third wave detector outputting C(k−1) as a resultof computation by elastic waves induced in the third wave transmissionmedium by the signals corresponding to the A[i] to A[i+k−1], the B[i] toB[i+k−1], and the C[i−1].
 19. The adder according to claim 18, whereineach of the first input sections, the second input sections, and thethird input sections includes an electrode pair composed of a firstelectrode and a second electrode, and each of the first wave detector,the second wave detector, and the third wave detector includes a pair ofcomb-shaped electrodes meshed with each other.
 20. The adder accordingto claim 19, wherein the comb-shaped electrodes are orthogonal topropagation direction of the elastic wave, and spacing between the firstelectrode and the second electrode is equal to spacing between the pairof comb-shaped electrodes in the propagation direction of the elasticwave.